is it really accurate to map the infant school as the whole site and the junior school as a node?

perhaps it could be a shared site with 2 nodes?

This track under the M1 is completely blocked off by a very tall gate with a sign saying “private land, no public access”

There is a fairly extensive array of permissive bridleways in the vicinity of Hoton, all on land owned by the Prestwold estate. I've added a few which i surveyed, but there are probably others particularly N to the King's Brook and to the S of the village.

Footpath sign is further S than where current mapping shows path joining the road, but as the former pub site is being re-developed the footpath is closed (and, may, get re-routed).

This track is not a public path. Footpath is shown the other side of the field on the OS map which is correct

This is not a public footpath. The Gate is often locked and the path shown following the brook does not exist.